"Mathropolis: Create Your Dream City!"

Design for Mastery Kit

NEW

All grades Project 2 weeks

"Mathropolis: Create Your Dream City!"

Julia K

A.2A

A.2B

A.2C

A.2D

A.2E

+ 10 more

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Purpose

This project aims to immerse students in a hands-on learning experience where they collaboratively design a city using mathematical concepts on a Cartesian plane. By engaging in this real-world application, students will deepen their understanding of graphing equations, systems of linear equations, and geometric principles while fostering critical thinking and problem-solving skills. The project encourages students to explore the practical implications of mathematics in urban planning, promoting creativity and innovation in developing efficient and functional city layouts. Through peer collaboration and self-directed learning, students will gain confidence in their abilities to apply mathematical knowledge to authentic challenges, preparing them for future academic and real-world endeavors.

Learning goals

Students will develop proficiency in writing and graphing linear equations, focusing on parallel and perpendicular lines to design efficient urban layouts. They will apply systems of linear equations to solve real-world city planning challenges, optimizing resources and space. Through self-directed learning, students will reflect on their progress, utilizing feedback to refine their city plans. They will engage in critical thinking to create innovative city designs that incorporate key mathematical concepts, fostering a sense of identity and belonging within their collaborative groups.

Standards

[Texas] A.2A - determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities
[Texas] A.2B - write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points
[Texas] A.2C - write linear equations in two variables given a table of values, a graph, and a verbal description
[Texas] A.2D - write and solve equations involving direct variation
[Texas] A.2E - write the equation of a line that contains a given point and is parallel to a given line
[Texas] A.2F - write the equation of a line that contains a given point and is perpendicular to a given line
[Texas] A.2G - write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined
[Texas] A.3A - determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1)
[Texas] A.3C - graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems
[Texas] A.3B - calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems
[Texas] A.3E - determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
[Texas] A.3F - graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

Competencies

Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.

Products

Students will collaboratively create a detailed 2D map of their planned city on a large poster, incorporating graphing skills and creativity. Each group will design unique city features while adhering to mathematical concepts such as parallel and perpendicular lines and systems of linear equations. The final product will be showcased during the 'City Showcase Day,' where students will present their city plans, explaining the mathematical reasoning and innovative solutions behind their designs.

Launch

Begin the project with an interactive 'Virtual City Tour' where students explore a simulated city online, identifying and discussing key features such as roads, landmarks, and transportation systems. Engage students in a discussion on how graphing equations on a Cartesian plane can be used to visualize and plan these elements, highlighting the role of parallel and perpendicular lines. Encourage students to brainstorm initial ideas for their own city plans, considering how mathematical concepts will guide their design process. This immersive experience will set the stage for students to embark on their city planning journey with a clear understanding of the project's goals and challenges.

Exhibition

Students will host a 'City Showcase Day' where they present their city plans to classmates, teachers, and local urban planners. Each group will set up a booth displaying their 2D city map on a large poster, explaining the mathematical concepts applied and the unique features of their city. Visitors will have the opportunity to ask questions and provide feedback, allowing students to demonstrate their understanding and creativity in urban planning.

Plan

Week 1	Day 1	Day 2	Day 3
Activities	Project Launch - Begin with a Virtual City Tour and discussion on graphing equations on a Cartesian plane to visualize city elements (30 min) Brainstorming Session - Students brainstorm initial ideas for their city plans, focusing on the role of parallel and perpendicular lines in urban planning (30 min) Group Formation - Form collaborative groups and outline the project goals and timeline, ensuring clarity on roles and responsibilities (30 min)	Graphing Basics Workshop - Review graphing linear equations and the use of Cartesian planes to set the foundation for city planning (30 min) Roads and Boundaries Design - Students practice writing and graphing linear equations to design roads and boundaries, focusing on parallel and perpendicular lines (45 min) Reflection and Feedback - Groups reflect on their designs and receive initial feedback from peers and teachers to refine their plans (15 min)	Creative Visualization Session - Use graphing software to visualize city layouts, identifying key features like x-intercepts and y-intercepts (45 min) Transformation Exploration - Experiment with transformations on the parent function f(x) = x and discuss impacts on city design (30 min) Daily Reflection - Reflect on the day's learning, focusing on how mathematical concepts are shaping city plans (15 min)
Deliverables	1. Completed initial draft of the 2D city layout on graph paper, incorporating parallel and perpendicular lines, and showcasing key city features identified during the Virtual City Tour.
Preparation	1. Prepare access to a virtual city simulation platform for the Virtual City Tour. 2. Gather graph paper, rulers, and markers for students to draft their city layouts. 3. Set up graphing software or online tools for students to visualize and modify their city designs. 4. Create a rubric for peer review sessions to guide constructive feedback on city layouts.

Week 2	Day 4	Day 5	Day 6
Activities	Final Design Refinement - Groups finalize their city plans, ensuring all mathematical concepts are accurately applied, focusing on parallel and perpendicular lines in transportation systems (45 min) Peer Critique Session - Exchange city plans with another group for constructive peer critique, highlighting strengths and areas for improvement in design and mathematical application (30 min) Feedback Incorporation - Incorporate peer and teacher feedback to make final adjustments to the city plan (15 min)	City Map Creation - Begin creating the final 2D map of the city on large posters, incorporating all design elements and mathematical concepts (45 min) Exhibition Preparation - Develop a presentation plan for the 'City Showcase Day,' detailing how mathematical concepts are integrated into the city design (30 min) Rehearsal and Reflection - Rehearse presentations and reflect on project learning goals, ensuring readiness to explain and discuss designs (15 min)	City Showcase Day Setup - Set up exhibition booths with completed city maps and prepare presentation materials for visitors (30 min) City Showcase Presentation - Present city plans to classmates, teachers, and local urban planners, explaining mathematical reasoning and unique city features (45 min) Feedback and Celebration - Engage with feedback from visitors and celebrate project completion with peers, reflecting on the learning journey and project outcomes (15 min)
Deliverables	1. Completed 2D city map poster with all mathematical equations and design features plotted. 2. Documentation of domain and range values for city features, represented using inequalities. 3. Presentation plan and visual aids for the City Showcase Day.
Preparation	1. Gather materials for poster creation, including large poster paper, markers, rulers, and graphing tools. 2. Ensure access to graphing software or applications for visualization and refinement of city layouts. 3. Organize peer feedback sessions and critique guidelines to facilitate constructive exchanges. 4. Prepare rehearsal space and equipment for presentation practice, such as projectors and screens.